AP Statistics / Mr. Hansen	Name: _______________________________________
11/16/2010	Mr. Hansen’s use only (bonus point for spare batteries): _______

Test on Probability (100 pts.)

• Calculator is OK throughout.
• If a blank is provided, give the short answer that fits best.
• If a gap is provided, provide adequate justification/explanation, and circle your answer.

1.	We will draw 2 cards, without replacement, from a well-shuffled deck. Let A be the event that a 7 is drawn on the first draw, and let B be the event that an 8 is drawn on the second draw. Are A and B mutually exclusive? (Write “yes” or “no.”) _______ Are A and B independent? _______ Compute , correct to 6 decimal places: _______
2.	In the Physics Egg Drop Competition, conducted by Dr. Morse, the probability of a completely unscathed egg was 0.6, and the probability of an egg being unscathed or only cracked was 0.76. All other eggs were smashed. Let U be the universe of all eggs that were dropped yesterday. Draw a Venn diagram to illustrate the universe, as well as the relationship among events G (good drop), O (OK drop with no more than a crack), and S (smashed). Use the blank region below. Also state the following to 3 decimal places of accuracy: = _______ P(G | O) = _______ P(O | G) = _______ P(S) = _______ = _______ Explain carefully why S and G are mutually exclusive but not independent. Label the probabilities that you use in your proof.
3.	Two fair dice are rolled. Compute the probability of an even sum, given that neither die is a 1. Show your work (no credit without work).
4.	I feel lucky, and I think I can roll snake eyes (double 1) on my next roll of the dice. You offer to bet me with payout odds of 35:1. Is this a fair game? _______ Optional bonus: Compute the expected value of the game for each dollar that I wager. (Work is needed for credit.)
5.	Tell me (in extremely general terms) how you would approach the following question. Use the words “probability” and “sample proportion” in your answer. DO NOT SOLVE. DO NOT WRITE A DETAILED SOLUTION. However, do use the required terms in your answer. An airplane has 100 passenger seats. However, no obese person can board if 2 or more obese people are already seated on that side of the fuselage. The fuselage has 2 sides (left and right, with 50 seats on each side). All 100 seats are reserved and assigned to passengers, 10% of whom are obese. We wish to know the probability that the third obese passenger to attempt to board will be denied boarding.